Optimal Quantization of TV White Space Regions for a Broadcast Based Geolocation Database

In the current paradigm, TV white space databases communicate the available channels over a reliable Internet connection to the secondary devices. For places where an Internet connection is not available, such as in developing countries, a broadcast based geolocation database can be considered. This geolocation database will broadcast the TV white space (or the primary services protection regions) on rate-constrained digital channel. In this work, the quantization or digital representation of protection regions is considered for rate-constrained broadcast geolocation database. Protection regions should not be declared as white space regions due to the quantization error. In this work, circular and basis based approximations are presented for quantizing the protection regions. In circular approximation, quantization design algorithms are presented to protect the primary from quantization error while minimizing the white space area declared as protected region. An efficient quantizer design algorithm is presented in this case. For basis based approximations, an efficient method to represent the protection regions by an `envelope' is developed. By design this envelope is a sparse approximation, i.e., it has lesser number of non-zero coefficients in the basis when compared to the original protection region. The approximation methods presented in this work are tested using three experimental data-sets.Comment: 8 pages, 12 figures, submitted to IEEE DySPAN (Technology) 201

Evaporation and Accretion of Extrasolar Comets Following White Dwarf Kicks

Several lines of observational evidence suggest that white dwarfs receive small birth kicks due to anisotropic mass loss. If other stars possess extrasolar analogues to the Solar Oort cloud, the orbits of comets in such clouds will be scrambled by white dwarf natal kicks. Although most comets will be unbound, some will be placed on low angular momentum orbits vulnerable to sublimation or tidal disruption. The dusty debris from these comets will manifest itself as an IR excess temporarily visible around newborn white dwarfs; examples of such disks may already have been seen in the Helix Nebula, and around several other young white dwarfs. Future observations with the James Webb Space Telescope may distinguish this hypothesis from alternatives such as a dynamically excited Kuiper Belt analogue. Although competing hypotheses exist, the observation that $\gtrsim 15\%$ of young white dwarfs possess such disks, if interpreted as indeed being cometary in origin, provides indirect evidence that low mass gas giants (thought necessary to produce an Oort cloud) are common in the outer regions of extrasolar planetary systems. Hydrogen abundances in the atmospheres of older white dwarfs can, if sufficiently low, also be used to place constraints on the joint parameter space of natal kicks and exo-Oort cloud models.Comment: 22 pages, 13 figures, published in MNRAS. Changes made to match published versio

Adaptive nonparametric confidence sets

We construct honest confidence regions for a Hilbert space-valued parameter in various statistical models. The confidence sets can be centered at arbitrary adaptive estimators, and have diameter which adapts optimally to a given selection of models. The latter adaptation is necessarily limited in scope. We review the notion of adaptive confidence regions, and relate the optimal rates of the diameter of adaptive confidence regions to the minimax rates for testing and estimation. Applications include the finite normal mean model, the white noise model, density estimation and regression with random design.Comment: Published at http://dx.doi.org/10.1214/009053605000000877 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org